Three-dimensional object data generation apparatus, three-dimensional object forming apparatus, and non-transitory computer readable medium

ABSTRACT

A three-dimensional object data generation apparatus includes an obtaining unit that obtains three-dimensional object data which represents, with plural voxels, a three-dimensional object including a shape obtained by repeating a unit shape and in which an attribute value is set for each of the plural voxels, a setting unit that sets a three-dimensional threshold matrix in which thresholds are arranged in a three-dimensional space in accordance with a predetermined basic shape, a correction unit that corrects a coordinate value of each of the plural voxels in a certain direction of the three-dimensional object such that the unit shape is formed from a first reference position in the certain direction, and a calculation unit that calculates, on a basis of the attribute value of each of the plural voxels whose coordinate values have been corrected and the three-dimensional threshold matrix, whether to form the voxel.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based on and claims priority under 35 USC 119 from Japanese Patent Application No, 2018-207514 filed Nov. 2, 2018.

BACKGROUND (i) Technical Field

The present disclosure relates to a three-dimensional object data generation apparatus, a three-dimensional object forming apparatus, and a non-transitory computer readable medium.

(ii) Related Art

Japanese Unexamined Patent Application Publication No. 2017-109427 discloses a solid body forming apparatus including a dot forming unit that forms dots included in a solid body to be formed and a support member that supports the solid body and a control unit that controls the forming of the solid body and the support member including the dots. The control unit arranges the dots in a voxel group that represents the support member on the basis of an input value indicating a forming ratio of the dots in voxels included in the voxel group and a dither mask such that a support structure that supports the solid body is formed.

Japanese Unexamined Patent Application Publication No. 2017-30177 discloses a solid body forming apparatus that includes a head unit capable of discharging liquid, a curing unit that forms dots by curing the liquid discharged from the head unit, and a forming control unit that controls operation of the head unit such that a solid body is formed as a group of dots by representing a shape of the solid body to be formed with a voxel group and forming the dots in voxels, in the voxel group, determined by a determination unit as voxels in which the dots are to be formed. The determination unit determines the voxels in which the dots are to be formed in accordance with a forming index, which is a value according to a forming ratio of the dots in voxels in the voxel group inside the solid body and a result of comparison with a threshold included in the dither mask.

Japanese Unexamined Patent Application Publication No. 2018-1725 discloses a three-dimensional data generation apparatus including a measurement result reception unit that receives a result of measurement of a shape of a first object output from an output apparatus using first three-dimensional data specifying the shape of the first object, a correction data calculation unit that calculates correction data on the basis of an error from the shape specified by the first three-dimensional data corresponding to the result of measurement received by the measurement result reception unit, and a data correction unit that corrects second three-dimensional data specifying a shape of a second object using the correction data calculated by the correction data calculation unit.

SUMMARY

If whether to form each of a plurality of voxels representing a three-dimensional object including a shape obtained by repeating a unit shape is calculated on the basis of a result of comparison between an intensity value set for the voxel and a corresponding threshold in a three-dimensional threshold matrix, for example, parts of unit shapes might be undesirably omitted. If the parts of the unit shapes are omitted, a desired function or a desired property might not be eyed.

Aspects of non-limiting embodiments of the present disclosure relate to a three-dimensional object data generation apparatus, a three-dimensional object forming apparatus, and a non-transitory computer readable medium capable of suppressing omission of parts of unit shapes when a three-dimensional object including a shape obtained by repeating a unit shape is formed.

Aspects of certain non-limiting embodiments of the present disclosure overcome the above disadvantages and/or other disadvantages not described above. However, aspects of the non-limiting embodiments are not required to overcome the disadvantages described above, and aspects of the non-limiting embodiments of the present disclosure may not overcome any of the disadvantages described above.

According to an aspect of the present disclosure, there is provided a three-dimensional object data generation apparatus including an obtaining unit that obtains three-dimensional object data which represents, with a plurality of voxels, a three-dimensional object including a shape obtained by repeating a unit shape and in which an attribute value is set for each of the plurality of voxels, a setting unit that sets a three-dimensional threshold matrix in which thresholds are arranged in a three-dimensional space in accordance with a predetermined basic shape, a correction unit that corrects a coordinate value of each of the plurality of voxels in a certain direction of the three-dimensional object such that the unit shape is formed from a first reference position in the certain direction, and a calculation unit that calculates, on a basis of the attribute value of each of the plurality of voxels whose coordinate values have been corrected and the three-dimensional threshold matrix, whether to form the voxel.

BRIEF DESCRIPTION OF THE DRAWINGS

An exemplary embodiment of the present disclosure will be described in detail based on the following figures, wherein:

FIG. 1 is a diagram illustrating the configuration of a three-dimensional object forming system;

FIG. 2 is a diagram illustrating the electrical configuration of a three-dimensional object data generation apparatus;

FIG. 3 is a block diagram illustrating the functional configuration of the three-dimensional object data generation apparatus;

FIG. 4 is a diagram illustrating an example of a three-dimensional object represented by voxel data;

FIG. 5 is a diagram illustrating the configuration of a three-dimensional object forming apparatus;

FIG. 6 is a flowchart illustrating a process achieved by a program for generating three-dimensional object data;

FIG. 7 is a diagram illustrating an example of a three-dimensional threshold matrix;

FIG. 8 is a diagram illustrating an example of threshold tables included in the three-dimensional threshold matrix;

FIG. 9 is a diagram illustrating presence or absence of discharging of an object material;

FIG. 10 is a diagram illustrating an example of a basic shape;

FIG. 11 is a diagram illustrating presence or absence of discharging of an object material;

FIG. 12 is a diagram illustrating another example of the basic shape;

FIG. 13 is a diagram illustrating correction of a coordinate value along a Z axis;

FIG. 14 is a diagram illustrating an example of a threshold matrix, first attribute values, and second attribute values;

FIG. 15 is a diagram illustrating another example of the threshold matrix, the first attribute values, and the second attribute values;

FIG. 16 is a diagram illustrating another example of the threshold matrix, the first attribute values, and the second attribute values;

FIG. 17 is a diagram illustrating another example of the threshold matrix, the first attribute values, and the second attribute values;

FIG. 18 is a diagram illustrating an example of omission of parts of unit shapes;

FIG. 19 is a diagram illustrating setting of a threshold matrix according to a correction coefficient;

FIG. 20 is a perspective view of an airtight hollow structure; and

FIG. 21 is a perspective view of a bending beam structure.

DETAILED DESCRIPTION

An exemplary embodiment of the present disclosure will be described hereinafter with reference to the drawings.

FIG. 1 is a diagram illustrating the configuration of a three-dimensional object forming system 1 according to the present exemplary embodiment. As illustrated in FIG. 1, the three-dimensional object forming system 1 includes a three-dimensional object data generation apparatus 10 and a three-dimensional object forming apparatus 100.

Next, the configuration of the three-dimensional object data generation apparatus 10 according to the present exemplary embodiment will be described with reference to FIG. 2.

The three-dimensional object data generation apparatus 10 is a personal computer, for example, and includes a controller 12. The controller 12 includes a central processing unit (CPU) 12A, a read-only memory (ROM) 12B, a random-access memory (RAM) 12C, a nonvolatile memory 12D, and an input/output (I/O) interface 12E. The CPU 12A, the ROM 12B, the RAM 12C, the nonvolatile memory 12D, and the I/O interface 12E are connected to one another through a bus 12F.

An operation unit 14, a display unit 16, a communication unit 18, and a storage unit 20 are connected to the i/o interface 12E.

The operation unit 14 includes, for example, a mouse and a keyboard.

The display unit 16 is, for example, a liquid crystal display.

The communication unit 18 is an interface for communicating data with external apparatuses such as the three-dimensional object forming apparatus 100.

The storage unit 20 is a nonvolatile storage device such as a hard disk and stores a program for generating three-dimensional object data, which will be described later, three-dimensional object data (voxel data), and three-dimensional threshold matrices, which will be described later, and the like. The CPU 12A reads the program for generating three-dimensional object data stored in the storage unit 20 and executes the program.

Next, the functional configuration of the CPU 12A will be described.

As illustrated in FIG. 3, the CPU 12A includes an obtaining unit 50, a correction unit 51, a setting unit 52, an adjustment unit 54, a calculation unit 56, and a reception unit 58 in terms of functions.

The obtaining unit 50 obtains three-dimensional object data that represents, with a plurality of voxels, a three-dimensional object including a shape obtained by repeating a unit shape and in which an attribute value is set for each of the plurality of voxels by reading the three-dimensional object data from the storage unit 20.

A correction unit 51 corrects coordinate values of a plurality of voxels in a certain direction of a three-dimensional object such that unit shapes are formed from a first reference position in the certain direction.

The setting unit 52 sets a three-dimensional threshold matrix in which thresholds are arranged in a three-dimensional space in accordance with a predetermined basic shape by reading the three-dimensional threshold matrix from the storage unit 20.

The adjustment unit 54 adjusts a cycle of the three-dimensional threshold matrix set by the setting unit 52 in accordance with attribute values. More specifically, the adjustment unit 54 adjusts the cycle of the three-dimensional threshold matrix using adjustment coefficients for setting degrees of adjustment of the cycle of the three-dimensional threshold matrix.

The calculation unit 56 calculates, on the basis of the attribute value of each of the plurality of voxels whose coordinate values have been corrected by the correction unit 51 and the three-dimensional threshold matrix, whether to form the voxel and stores a result of the calculation in the storage unit 20. If the adjustment unit 54 has adjusted the cycle of the three-dimensional threshold matrix, the calculation unit 56 uses the three-dimensional threshold matrix whose cycle has been adjusted by the adjustment unit 54.

The reception unit 58 receives adjustment coefficients specified by a user by operating the storage unit 14, details of which will be described later.

If the reception unit 58 receives adjustment coefficients, the adjustment unit 54 adjusts the cycle of the three-dimensional threshold matrix using the adjustment coefficients in accordance with the attribute values of the voxels.

A case will be described in the present exemplary embodiment where an intensity value indicating the intensity of each voxel is set for the voxel as a first attribute value and whether to form the voxel is calculated as a second attribute value.

FIG. 4 illustrates a three-dimensional object 32 represented by three-dimensional object data (voxel data), which is a group of voxels. As illustrated in FIG. 4, the three-dimensional object 32 includes a plurality of voxels 34.

The voxels 34 are basic elements of the three-dimensional object 32. The voxels 34 may be rectangular parallelepipeds, for example, but may be spheres or cylinders, instead. A desired three-dimensional object is represented by stacking the voxels 34 on one another.

As a method for forming a three-dimensional object, for example, fused deposition modeling (FDM), in which a thermoplastic resin is plasticized and stacked to form a three-dimensional object, or selective laser sintering (SLS), in which a laser beam is radiated onto a powdery metal material to form a three-dimensional object through sintering, is used, but another method may be used, instead. In the present exemplary embodiment, a case where a three-dimensional object is formed using FDM will be described.

Next, a three-dimensional object forming apparatus that forms a three-dimensional object using three-dimensional object data generated by the three-dimensional object data generation apparatus 10 will be described.

FIG. 5 illustrates the configuration of the three-dimensional object forming apparatus 100 according to the present exemplary embodiment. The three-dimensional object forming apparatus 100 forms a three-dimensional object using FDM.

As illustrated in FIG. 5, the three-dimensional object forming apparatus 100 includes a discharge head 102, a discharge head driving unit 104, a stand 106, a stand driving unit 108, an obtaining unit 110, and a control unit 112. The discharge head 102, the discharge head driving unit 104, the stand 106, and the stand driving unit 108 are an example of a forming unit.

The discharge head 102 includes an object material discharge head that discharges an object material for forming a three-dimensional object 40 and a support material discharge head that discharges a support material. The support material is used to support overhangs (also referred to as “projections”) of the three-dimensional object 40 and removed after the three-dimensional object 40 is formed.

The discharge head 102 is driven by the discharge head driving unit 104 and moves on an X-Y plane in two dimensions. The object material discharge head may include a plurality of discharge heads corresponding to object materials of a plurality of attributes (e.g., colors).

The stand 106 is driven by the stand driving unit 108 and moves in a Z-axis direction.

The obtaining unit 110 obtains three-dimensional object data and support material data generated by the three-dimensional object data generation apparatus 10.

The control unit 112 drives the discharge head driving unit 104 to move the discharge head 102 in two dimensions and controls the discharge of the object material and the support material performed by the discharge head 102 such that the object material is discharged in accordance with the three-dimensional object data obtained by the obtaining unit 110 and the support material is discharged in accordance with the support material data obtained by the obtaining unit 110.

Each time a layer has been formed, the control unit 112 drives the stand driving unit 108 to lower the stand 106 by a predetermined layer interval. As a result, a three-dimensional object based on three-dimensional object data is formed.

Next, the operation of the three-dimensional object data generation apparatus 10 according to the present exemplary embodiment will be described with reference to FIG. 6. A generation process illustrated in FIG. 6 is performed by causing the CPU 12A to execute a program for generating three-dimensional object data. The generation process illustrated in FIG. 6 is performed, for example, when the user has requested execution of the program. In the present exemplary embodiment, description of a process for generating support material data and support material route data is omitted.

In step S100, voxel data corresponding to a three-dimensional object to be formed is read, for example, from the storage unit 20. Alternatively, voxel data may be obtained from an external apparatus using the communication unit 18.

In step S102, three-dimensional object display data is generated from the voxel data obtained in step S100 and displayed on the display unit 16.

In step S103, the display unit 16 displays a screen for receiving adjustment coefficients, which will be described later, and receives adjustment coefficients input by the user. The adjustment coefficient are set for three axes, namely X, Y, and Z axes, which are perpendicular to one another. The user may input an adjustment coefficient for each of the X, Y, and Z axes, or a single input adjustment coefficient may be automatically set for all the axes.

In step S104, a three-dimensional threshold matrix used to calculate whether to form each voxel is set. In the three-dimensional threshold matrix, thresholds are arranged in a three-dimensional space in accordance with a predetermined basic shape.

FIG. 7 illustrates a three-dimensional threshold matrix M as an example. As illustrated in FIG. 7, the three-dimensional threshold matrix M includes seven layers of threshold tables Z1 to Z7.

FIG. 8 illustrates an example of the threshold tables Z1 to Z7. As described later, when whether to form each voxel is calculated, the same process as so-called “halftone” is performed on voxel data in layers corresponding to the threshold tables Z1 to Z7 with the threshold tables Z1 to Z7 set as dither matrices. That is, each threshold in the threshold tables Z1 to Z7 and an intensity value of a corresponding voxel are compared with each other. If the intensity value is equal to or larger than the threshold, the voxel is to be formed, and if the intensity value is smaller than the threshold, the voxel is not to be formed. It is assumed in the present exemplary embodiment that a value that can be taken by an intensity value is equal to or larger than 0. If the threshold is 0, a voxel corresponding to the threshold will be invariably formed. Parts where thresholds are 0, therefore, correspond to the basic shape.

In the example illustrated in FIG. 8, a threshold of 0 is set at the center of every layer, and in the fourth threshold table Z4, which is a central layer in the Z-axis direction, a threshold of 0 is set on an X-Y plane in a shape of a cross. That is, thresholds at positions corresponding to the basic shape are set to a minimum value of a possible range of thresholds. If intensity values of voxels are all 0 in the three-dimensional threshold matrix M, therefore, an object material is discharged at positions indicated by solid squares illustrated in FIG. 9. As a result, the basic shape of the three-dimensional threshold matrix M becomes a basic shape K illustrated in FIG. 10.

As illustrated in FIG. 8, thresholds in the threshold tables Z1 to Z7 other than those at the positions corresponding to the basic shape are all 35 or larger. If the intensity values of the voxels are all smaller than 35, therefore, the basic shape K illustrated in FIG. 1 obtained. If the intensity values of the voxels are all 50, on the other hand, an object material is discharged at positions indicated by solid squares illustrated in FIG. 11. As a result, as illustrated in FIG. 12, the basis shape of the three-dimensional threshold matrix M becomes a basic shape K2, which is thicker than the basic shape K illustrated in FIG. 10.

As illustrated in FIG. 8, the thresholds set in the threshold tables Z1 to Z7 other than those at the positions corresponding to the basic shape are larger in the periphery. This means that the thresholds set in the three-dimensional threshold matrix M are smaller at the center of the three-dimensional space indicated by the three-dimensional threshold matrix M and larger in the periphery. That is, because of the thresholds set in the three-dimensional threshold matrix M, the percentage of voxels to be formed is lower in the periphery of the three-dimensional space indicated by the three-dimensional threshold matrix M. In other words, the thresholds are set such that intensity becomes higher at the center of the three-dimensional space indicated by the three-dimensional threshold matrix M. As the three-dimensional threshold matrix M becomes smaller, the basic shape becomes smaller and a resultant three-dimensional object becomes denser and harder. As the three-dimensional threshold matrix M becomes larger, on the other hand, the basic shape becomes larger and a resultant three-dimensional object becomes thinner and softer. If the user desires to make a certain part hard, therefore, the user may set a small three-dimensional threshold matrix, and if the user desires to make a certain part soft, the user may set a large three-dimensional threshold matrix.

In the present exemplary embodiment, the storage unit 20 stores various three-dimensional threshold matrices corresponding to various basic shapes. The user operates the operation unit 14 to select a desired basic shape, that is, a desired three-dimensional threshold matrix. The number of three-dimensional threshold matrices to be selected need not be one, and a plurality of three-dimensional threshold matrices may be selected for each part of a three-dimensional object, instead.

In step S105, a coordinate value of each of a plurality of voxels in a certain direction of the three-dimensional object corrected such that unit shapes are formed from a first reference position in the certain direction. In the present exemplary embodiment, a case will be described, for example, where the certain direction is the Z-axis direction and the first reference position is a bottom plane in the Z-axis direction of the three-dimensional object. In addition, in the present exemplary embodiment, a case will be described, for example, where the three-dimensional object represented by the three-dimensional object data obtained in step S100 is a three-dimensional object 60 illustrated in FIG. 13. FIG. 13 illustrates a part of the three-dimensional object 60. As illustrated in FIG. 13, the three-dimensional object 60 includes, on a base member A, two layers of repeated unit shapes 62-1 and 62-2. In the following description, the unit shapes 62-1 and 62-2 will be simply referred to as “unit shapes 62” if not distinguished from each other. Although the unit shapes 62 are hollow spheres in the present exemplary embodiment, the unit shapes 62 are not limited to hollow spheres.

Although the unit shapes 62 are arranged on an X-Z plane in two-dimensions in FIG. 13, the unit shapes 62 are also arranged on the X-Y plane and a Y-Z plane in two dimensions. At this time, the first reference position is a coordinate of the base member A in the Z-axis direction.

If the first attribute value of a voxel is denoted by V1(i, j, k) and coordinate values along the X, Y, and Z axes are denoted by i, j, and k, respectively, the coordinate value k along the Z-axis is corrected using the following expression. k=k−k0  (1)

Here, k0 is a phase term and represented by the following expression. k0=Z _(A)(i,j)/Vp  (2)

Here, Z_(A)(i, j) denotes the coordinate value of the base member A along the Z axis at the coordinate value i along the x axis and the coordinate value j along the Y axis. Vp denotes intervals of voxels in the Z-axis direction, which is the certain direction. That is, Vp denotes the length of each voxel in the Z-axis direction.

The phase term k0 thus has a role of normalizing the coordinate value k of the first attribute value V1(i, j, k) along the Z axis with the coordinate value Z_(A)(i, of the base member A along the Z axis.

In step S105, whether to form each of the plurality of voxels is calculated on the basis of the intensity value set for the voxel whose coordinate value has been corrected in step S105, the three-dimensional threshold matrix set in step S104, and the adjustment coefficients received in step S103. More specifically, as described above, the same process as so-called “halftone” is performed on the voxel data in layers corresponding to the threshold tables Z1 to Z7 with the threshold tables Z1 to Z7 set as dither matrices, That is, each threshold in the threshold tables Z1 to Z7 and the intensity value of the voxel at a corresponding position are compared with each other. If the intensity value is equal to or larger than the threshold, the voxel is to be formed, and if the intensity value is smaller than the threshold, the voxel is not to be formed.

Whether each voxel is to be formed is calculated using the following expressions, where the first attribute value of the voxel is denoted by V1(i, j, k), the corresponding threshold in the three-dimensional threshold matrix is denoted by Mt(l, m, n), and the second attribute value is denoted by V2(i, j, k). V2(i,j,k)=VmaxP,V1(i,j,k)<Mt(l,m,n)  (3) V2(i,j,k)VmaxM,V1(i,j,k)≥Mt(l,m,n)  (4)

Here, i, j, and k denote coordinate values of the X, Y, and Z axes, respectively. l, m, and n denote X, Y, and Z coordinate values, respectively, of the threshold in the three-dimensional coordinate matrix and are expressed as follows. l=MOD(Ax×i,Mx)  (5) m=MOD(Ay×j,My)  (6) n=MOD(Az×k,Mz)  (7)

MOD(a, b) denotes a residue at a time when a has been divided by b. Therefore, l denotes a residue at a time when Ax×i has been divided by Mx. Similarly, m denotes a residue at a time when Ay×j has been divided by My, and n denotes a residue at a time when Az×k has been divided by Mz. Mx denotes the size of the three-dimensional threshold matrix in an X-axis direction, that is, the number of thresholds in the X-axis direction. Similarly, My denotes the size of the three-dimensional threshold matrix in a Y-axis direction, that is, the number of thresholds in the Y-axis direction, and Mz denotes the size of the three-dimensional threshold matrix in the Z-axis direction, that is, the number of thresholds in the Z-axis direction.

Ax, Ay, and Ax are expressed as follows. Ax=Ax0×V1(i,j,k)/VmaxP+1  (8) Ay=Ay0×V1(i,j,k)/VmaxP+1  (9) Az=Az0×V1(i,j,k)/VmaxP+1  (10)

Ax0 is the adjustment coefficient for the X axis, Ay0 is the adjustment coefficient for the Y axis, and Az0 is the adjustment coefficient for the Z axis. 0≤Ax0≤Bx, 0≤Ay0≤By, and 0≤Az0≤Bz. Ex denotes a maximum value of the adjustment coefficient Ax. Similarly, By and Bz denote maximum values of the adjustment coefficients Ay and Az, respectively. Although a case where Bx=By=Bz=1 will be described in the present exemplary embodiment as an example, the maximum values of the adjustment coefficients are not limited to 1. If all the adjustment coefficients are 0, that is, if Ax0=Ay0=Az0=0, the cycle of the three-dimensional threshold matrix is not adjusted. As an adjustment coefficient becomes larger from 0, a degree of adjustment becomes larger. In order to increase a maximum value of the degree of adjustment, therefore, Bx, By, or Bz is increased.

VmaxM is a value obtained by adding a minus sign “−” to a maximum value of V1(i, j, k). In the present exemplary embodiment, V1(i, j, k) is expressed in 8 bits, for example, and can take a value of 0 to 255. VmaxM, therefore, is −255. VmaxP is a value obtained by adding a plus sign “+” to a maximum value of V1(l, j, k). VmaxP, therefore, is +255. VmaxM indicates that a voxel is not to be formed, and VmaxP indicates that a voxel is to be formed.

If the first attribute value V1(i, j, k) is smaller than the threshold Mt(1, m, n), the second attribute value V2(i, j, k) becomes VmaxM, and a voxel is not to be formed. If the first attribute value V1(j, k) is equal to or larger than the threshold Mt (l, m, n), the second attribute value V2(i, j, k) becomes VmaxP, and a voxel is to be formed.

As illustrated in FIG. 14, for example, a case where a threshold matrix Mt1 and the first attribute values V1 of voxels are compared with each other will be described. Here, the adjustment coefficients are Ax0−Ay0−Az0=0, that is, a cycle of the three-dimensional threshold matrix Mt1 is not adjusted.

The three-dimensional threshold matrix Mt1 illustrated in FIG. 14 includes various values such that the thresholds gradually change from the threshold of 0, which corresponds to the basic shame. More specifically, the three-dimensional threshold matrix Mt1 includes four different thresholds of 0, 80, 160, and 255. The larger the distance from the threshold of 0, which corresponds to the basic ape, the larger the threshold. It is assumed here that the first attribute values V1 of the voxels are uniformly 70, this case, as illustrated in FIG. 14, the second attribute values V2 of central voxels in the X-axis direction and the Y-axis direction indicate that a voxel is to be formed, thereby forming a shape of a cross.

It is also assumed that the first attribute values V1 of the voxels are uniformly 90 as illustrated in FIG. 15. In tris case, the second attribute values V2 of three central voxels in the X-axis direction and the Y-axis direction indicate that a voxel is to be formed, thereby forming a shape of a cross thicker than that illustrated in FIG. 14.

Next, as illustrated in FIG. 16, a case will be described where a threshold matrix Mt2 in which two different thresholds, namely a first threshold of 0 corresponding to the basic shape and a second threshold of 255 corresponding to a shape other than the basic shape, are set is used. The adjustment coefficients are Ax0=Ay0 Az0=0, that is, a cycle of the three-dimensional threshold matrix Mt2 is not adjusted.

As illustrated in FIG. 16, the first attribute values V1 vary within a range of 0 to 255 in such a way as to become larger in a right part of FIG. 16 in the X-axis direction. Since the cycle of the three-dimensional threshold matrix Mt2 is not adjusted here, the second attribute values V2 of voxels corresponding to two basic shapes simply arranged side-by-side in the X-axis direction indicate, as illustrated in FIG. 16, that a voxel is to be formed.

If, in the example illustrated in FIG. 16, the adjustment coefficients become Ax0=Ay0=Az0=1, that is, the cycle of the three-dimensional threshold matrix Mt2 is adjusted, a coordinate scale of the three-dimensional threshold matrix Mt2 compared with the first attribute values V1 changes. As a result, as illustrated in FIG. 17, the second attribute values V2 of voxels corresponding to basic shapes that become denser in a right part in the X-axis direction indicate that a voxel is to be formed.

As described above, in the present exemplary embodiment, the coordinate value k of the first attribute value V1(i, j, k) of each voxel along the Z axis is corrected using expression (1). If the coordinate value k along the Z axis is not corrected using expression (1), lower parts the unit shapes 62-1 to be arranged on the base member A might be undesirably omitted as illustrated in FIG. 18. In the present exemplary embodiment, on the other hand, the coordinate value k of the first attribute value V1(i, j, k) of each voxel along the Z axis is corrected using expression (1) such that the unit shapes 62-1 are formed on the base member A, which is the first reference position in the Z-axis direction. As a result, as illustrated in FIG. 13, the unit shapes 62-1 are arranged on the base member A without omission.

Even if the correction is performed as described above, upper parts of the unit shapes 62-2, which are in a second layer from the base member A in the Z-axis direction, might be undesirably omitted as illustrated in FIG. 18.

The corrected coordinate value k along the Z axis may be further corrected using a correction coefficient b so that an integer number of unit shapes 62 are obtained in the z-axis direction, which is the certain direction.

More specifically, the coordinate value k is corrected using the following expression. k=b(k−k0)  (11)

That is, the coordinate value k corrected using expression (1) is further corrected by multiplying the coordinate value k by the correction coefficient b.

More specifically, the correction coefficient b is calculated using following expression.

$\begin{matrix} {b = \frac{B}{{roundup}\mspace{14mu}(B)}} & (12) \end{matrix}$

Here, roundup(B) denotes a function for rounding upward the number B of unit shapes 62 in the Z-axis direction. The number B is calculated us the following expression.

$\begin{matrix} {B = \frac{{\int_{Z_{A}}^{Z_{A^{\prime}}}{\left( {1/{Az}} \right){dz}}}\ }{\int_{Z_{A}}^{Z_{A^{\prime}}}{dz}}} & (13) \end{matrix}$

Here, Az is denoted by expression (10). Z_(A) is specifically Z_(A)(1, j) mentioned above and denotes the coordinate value of the base member A along the Z axis at the coordinate value i along the X axis and the coordinate value j along the Y axis. Z ‘ is specifically Z_(A)′(i, j) and, as illustrated in FIG. 13, denotes a coordinate value of a top plane A’ along the Z axis at the coordinate value along the X axis and the coordinate value j along the Y axis. The top plane A° is in contact with upper parts of the unit shapes 62-2 in a top layer in the Z-axis direction.

If B=1.5, for example, roundup(1.5)=2, and b=0.75 from expression (12). The coordinate value k is therefore obtained by multiplying the coordinate value k corrected using expression (1) by 0.75, As a result, the length of the unit shapes 62 in the Z-axis direction is reduced to 75%.

The correction coefficient b is thus used to reduce the unit shapes in size such that an integer number of unit shapes 62 are obtained between the base member A, which is the first reference position, and the top plane A′, which is a second reference position in the Z-axis direction.

Alternatively, a function rounddown(B) for rounding downward the number B may be used instead of the function roundup(B) in expression (12). If B=1.5 in this case, for example, rounddown(B)=1, and b=2 from expression (12). In this case, the coordinate value k is obtained by multiplying the coordinate value k corrected using expression (1) by 1.5. As a result, the length of the unit shapes 62 in the Z-axis direction is increased to 150%. The correction coefficient b is thus used to increase the unit shapes 62 in size such that an integer number of unit shapes 62 are obtained between the base member A, which is the first reference position, and the top plane A′, which is the second reference position in the Z-axis direction.

Since an integer number of unit shapes 62 are obtained between the base member A and the top plane A′ by correcting the coordinate value k using expression (11), parts of the unit shapes 62 in the second layer are not omitted.

In step S108, data indicating whether to form each voxel calculated in step S106 is transmitted to the three-dimensional object forming apparatus 100 as voxel data.

The obtaining unit 110 of the three-dimensional object forming apparatus 100 obtains the voxel data transmitted from the three-dimensional object data generation apparatus 10. The control unit 112 drives the discharge head driving unit 104 to move the discharge head 102 in two dimensions and controls the discharge of the object material performed by the discharge head 102 such that the object material is discharged in accordance with the voxel data obtained by the obtaining unit 110. As a result, a three-dimensional object is formed.

Although the present disclosure has been described using an exemplary embodiment, the present disclosure is not limited to the above exemplary embodiment. The above exemplary embodiment may be modified or improved in various ways without deviating from the scope of the present disclosure. The technical scope of the present disclosure also includes such modifications and improvements.

If, as described above, the coordinate value k of the first attribute value V(i, j, k) is corrected using expression (11), for example, the unit shapes 62 are reduced or increased in size, and a resultant three-dimensional object might not have a desired property. For this reason, three-dimensional threshold matrices corresponding to various thicknesses of the basic shape set in accordance with the correction coefficient b, therefore, may be set, More specifically, as illustrated in FIG. 19, for example, a three-dimensional threshold matrix corresponding to a thicker basic shape is used as the correction coefficient b becomes larger, Since the unit shapes 62 are increased in size and the intensity thereof decreases as the correction coefficient becomes larger, a three-dimensional threshold matrix corresponding to a thick basic shape is used to offset the decrease in the intensity. As illustrated in FIG. 19, for example, if the correction coefficient b is close to 1 when a possible range of the correction coefficient b is 1 to 2, the three-dimensional threshold matrix Mt1 is used. If the correction coefficient is close to 1.5, the three-dimensional threshold matrix Mt2 corresponding to a basic shape thicker than in the case of the three-dimensional threshold matrix Mt1 is used. If the correction coefficient is close to 2, a three-dimensional threshold matrix Mt3 corresponding to a basic shape even thicker than in the case of the three-dimensional threshold matrix Mt2 is used. As a result, a property of a resultant three-dimensional object does not significantly deviate from a desired property.

The present disclosure is suitable, for example, for an airtight hollow structure illustrated in FIG. 20 and a bending beam structure illustrated in FIG. 21. In the airtight hollow structure, gummy hollow spheres are used as unit shapes, and a high restitution coefficient is achieved because of the action of air springs. The present disclosure is suitable because the elasticity of air springs is not obtained if parts of the hollow spheres are omitted. In the bending beam structure, when pressed from above, beams, which are unit shapes, are bent and come into contact with one another to increase rigidity. As a result, excessive deformation is suppressed, thereby achieving high durability. The present disclosure is suitable because the beams do not come into contact with each other and durability decreases if parts of the beams are omitted.

Although the three-dimensional object data generation apparatus 10 and the three-dimensional object forming apparatus 100 that forms a three-dimensional object on the basis of three-dimensional object data are separately provided in the above exemplary embodiment, the three-dimensional object forming apparatus 100 may have the function of the three-dimensional object data generation apparatus 10, instead.

That is, the obtaining unit 110 of the three-dimensional object forming apparatus 100 may obtain voxel data, and the control unit 112 may generate three-dimensional object data by performing the generation process illustrated in FIG. 6.

Alternatively, for example, the process for generating three-dimensional object data illustrated in FIG. 6 may be achieved by hardware such as an application-specific integrated circuit (ASIC). In this case, processing speed increases compared to when the process is achieved by software.

Although the program for generating three-dimensional object data is installed on the storage unit 20 in the above exemplary embodiment, the process need not be installed on the storage unit 20. The program according to the above exemplary embodiment may be provided in a computer readable storage medium, instead. For example, the program in the present disclosure may be provided in an optical disc such as a compact disc read-only memory (CD-ROM) or a digital versatile disc read-only memory (DVD-ROM) or a semiconductor memory such as a universal serial bus (USE) memory or a memory card. Alternatively, the program according to the above exemplary embodiment may be obtained from an external apparatus through a communication line connected to the communication unit 18.

The foregoing description of the exemplary embodiment of the present disclosure has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in the art. The embodiment was chosen and described in order to best explain the principles of the disclosure and its practical applications, thereby enabling others skilled in the art to understand the disclosure for various embodiments and with the various modifications as are suited to the particular use contemplated. It is intended that the scope of the disclosure be defined by the following claims and their equivalents. 

What is claimed is:
 1. A three-dimensional object forming apparatus comprising: a three-dimensional object data generation apparatus comprising: an obtaining unit that obtains three-dimensional object data which represents, with a plurality of voxels, a three-dimensional object including a shape obtained by repeating a unit shape and in which an attribute value is set for each of the plurality of voxels; a setting unit that sets a three-dimensional threshold matrix in which thresholds are arranged in a three-dimensional space in accordance with a predetermined basic shape; an adjustment unit that adjusts a cycle of applying the three-dimensional threshold matrix in accordance with the attribute value across a space of the unit shape; a correction unit that corrects a coordinate value of each of the plurality of voxels in a certain direction of the three-dimensional object such that the unit shape is formed from a first reference position in the certain direction; and a calculation unit that determines, based on the attribute value of each of the plurality of voxels whose coordinate values have been corrected and the three-dimensional threshold matrix, whether to form the voxel; and a forming unit that forms a three-dimensional object based on three dimensional object data generated by the three-dimensional object data generation apparatus.
 2. The three-dimensional object forming apparatus according to claim 1, wherein the correction unit further corrects, using a correction coefficient, the corrected coordinate value in the certain direction such that an integer number of unit shapes are obtained in the certain direction.
 3. The three-dimensional object forming apparatus according to claim 2, wherein the correction coefficient is used to increase or reduce the unit shape in size such that an integer number of unit shapes are obtained between the first reference position and a second reference position in the certain direction.
 4. The three-dimensional object forming apparatus according to claim 3, wherein the setting unit sets the three-dimensional threshold matrix corresponding to thickness of the basic shape set in accordance with the correction coefficient.
 5. The three-dimensional object forming apparatus according to Claim 1, wherein the adjustment unit adjusts the cycle of the three-dimensional threshold matrix in accordance with an adjustment coefficient for setting a degree of adjustment of the cycle of the three-dimensional threshold matrix.
 6. The three-dimensional object forming apparatus according to claim 5, wherein the adjustment coefficient is set for each of three axes of the three-dimensional space perpendicular to one another.
 7. The three-dimensional object forming apparatus according to claim 5, further comprising: a reception unit that receives the adjustment coefficient.
 8. The three-dimensional object forming apparatus according to claim 1, wherein the thresholds include two different thresholds, namely a first threshold corresponding to a center of the basic shape and a second threshold corresponding to location other than the center of the basic shape.
 9. The three-dimensional object forming apparatus according to claim 1, wherein the thresholds include various thresholds such that the thresholds gradually change from a threshold corresponding to a center of the basic shape.
 10. The three-dimensional object forming apparatus according to claim 1, wherein the unit shape has an elastic structure.
 11. The three-dimensional object forming apparatus according to claim 10, wherein the unit shape has a hollow structure.
 12. The three-dimensional object forming apparatus according to claim 10, wherein the unit shape has a beam structure. 